Interaction-induced Fermi surface deformations in quasi one-dimensional electronic systems

TL;DR

This paper develops a variational and renormalization group approach to analyze how interactions deform the Fermi surface in quasi-one-dimensional electronic systems, revealing different phases including Luttinger liquids, Fermi liquids, and Mott insulators.

Contribution

It introduces a novel variational method equivalent to renormalized perturbation theory for studying Fermi surface deformations due to interactions.

Findings

Irrelevant couplings tend to deform the Fermi surface to become more relevant.

Identifies three regimes: Luttinger liquid, Fermi liquid, and incommensurate spin-density wave.

At half-filling, a Mott insulator with a flat Fermi surface emerges.

Abstract

We consider serious conceptual problems with the application of standard perturbation theory, in its zero temperature version, to the computation of the dressed Fermi surface for an interacting electronic system. In order to overcome these difficulties, we set up a variational approach which is shown to be equivalent to the renormalized perturbation theory where the dressed Fermi surface is fixed by recursively computed counterterms. The physical picture that emerges is that couplings that are irrelevant tend to deform the Fermi surface in order to become more relevant (irrelevant couplings being those that do not exist at vanishing excitation energy because of kinematical constraints attached to the Fermi surface). These insights are incorporated in a renormalization group approach, which allows for a simple approximate computation of Fermi surface deformation in quasi one-dimensional electronic conductors. We also analyze flow equations for the effective couplings and quasiparticle weights. For systems away from half-filling, the flows show three regimes corresponding to a Luttinger liquid at high energies, a Fermi liquid, and a low-energy incommensurate spin-density wave. At half-filling Umklapp processes allow for a Mott insulator regime where the dressed Fermi surface is flat, implying a confined phase with vanishing effective transverse single-particle coherence. The boundary between the confined and Fermi liquid phases is found to occur for a bare transverse hopping amplitude of the order of the Mott charge gap of a single chain.